Jason Lisk over at The Big Lead gets to an idea that I've been tossing around before I had a chance to get to writing about it (and he writes about it well). The Jets should go for two on almost every touchdown. You have to figure Tim Tebow's chances of getting a two-point conversion are well over 60 percent. I also think this argument applies to the Carolina Panthers.

Posted by: Aaron Schatz on 28 Mar 2012

57 comments, Last at
04 Apr 2012, 8:02pm by
Scott C

Comments

I'm open unconventional thinking, but looking only at expected value is a simplistic way to analyze the issue. The actual value of a two point attempt will obviously never be 1.2 points -- it will either be 0 or 2 points. A strategy that maximizes total points scored may still result in more losses if the team is unlucky in the distribution of successes and failures. That is to say, the Jets could succeed more on two pointers in games where the score isn't close and fail more in games where it is close.

Or it may result in more wins if the team is lucky in the distribution of successes and failures. Focusing on the unlucky side is a "three things can happen, and two of them are bad" type of argument that downplays the potential for a competitive advantage.

As important as the potential statistical advantage, in my opinion, is the potential psychological advantage. The University of Oregon under Chip Kelly will routinely go for two if they score the first TD of the game, because if they get it, suddenly the other team feels like they're down by more than one score. If they miss, well, it's something they've prepared for.

Or it may result in more wins if the team is lucky in the distribution of successes and failures

Yes, but with the difference only being a fraction of a point, the number of games it will take until a team sees a significant advantage over kicking the extra point will be very large.

Which means that in general, it'll look like a wash, and the only thing it will do is cause a team's score to jitter around more. Which, for a good offense (which for the Jets, OK, is questionable) is not a good thing.

The problem here is that the distribution of points into games in football is not random, unlike most other sports. Football involves a lot of jockeying for wins instead of points, particularly late in the game, and for a team that wants to think of itself as a defensive, run-first team like the Jets, the late game should start fairly early.

Say you score first. You assume both you and your opponent are going to score an equal amount of touchdowns and field goals(given a low scoring game and no safeties, this covers most of the situations where 2-pt. conversions matter). Extra points are, for sake of argument, 100%, your 2-pts. are 60%, you're opponent's are 40%.

If you kick, you're opponent's best choice is to tie by responding with a kick.

Naturallay, this is a crass oversimplification, but it illustrates how it is very well possible how a strategy that optimizes points increases the amount of losses by creating 2 point wins and 1 point losses. This would be less relevant for a team like Carolina, with a more offensive identity, though how much is up in the air.

Scoring last and knowing the situation when you choose to kick or go for two is a large advantage. This only applies near the end of the game.

If you happen to be the team to score last, it would be to your advantage to have gone for two earlier in the game. This is why going for two is about expected value (i.e. success rate) earlier in the game, and about the specific score differential and time remaining late in the game.

Right, but the problem is that you don't score enough early in the game for expected value to average out on a game by game basis.

Most teams score between 2 and 3 touchdowns a game, at most. So between 1 and 2 of those are 'early'. Which means you're really talking about 1-2 additional points before the end of the game.

You might think that's a big deal, but I doubt it is as big as you would expect, because the base scores in football are all larger than that, so the only cases where it becomes a big improvement are when the score differential goes from 3 or less to greater than 3, and 8 or less to greater than 8 (or less if the team's trailing).

So if you think about it, by success rate you win out a fraction of the time, but because in most games, the amount that you win out won't actually improve things, in the end, it just isn't going to have that big an effect.

The variance of a team's score game to game is dominated by variance in TDs and making/missing FGs. It is not a trivial question.

To use your argument, you would have to first prove that the small variance introduced by more 2 pt attempts is orthogonal to strategy in the rest of the game. That is obviously not true. These things are intertwined, so it is not a trivial question.

Examples:
A team with 1 TD goes for 2, and fails. Later in the game they go for a TD instead of a FG, the net result of the first decision is an increase in score variance from either 7 or 10 to 6 or 12/13/14.

Examples:
A team with 1TD goes for 2 and makes it. Late in the game they choose to go for 3 instead of a TD as a result of the extra point. The score variance decreases as a result.

Chip Kelly also has the advantage of knowing his offense can throw up 40 points a game, so it's unlikely that 1 XP at the beginning of the game will have an impact. A lot of the teams don't have the talent that Oregon does, so Chip is pressing his advantage against bad teams when calling for 2 point plays. Last year Oregon played 4 teams with comparable talent- USC, LSU, Stanford and Wisconsin. The only time they went for 2 early was against Stanford. It's a little tougher to do that when you can only reasonably expect to score 3 TDs at most- there the points are more valuable.

I like the concept of what the article is saying, but I don't think it would work as well as expected. Eventually teams would prepare for the conversions and the conversion rate would fall back to normal levels. The biggest value would be as a decoy- teams are conditioned to expect XPs after scores, but if Tebow and the offense ran out for a conversion you could bait the other team into wasting a timeout.

Living in Carolina (but not really a Panthers fan) I get to watch the Cam Newton show every Sunday. And let me tell you, it is very entertaining. Even though everybody around me still expects a third and long draw to DeShaun Foster every time, we are very much anticipating what Newton and the Panthers can do with a full offseason of work.

That said, I'm ALWAYS screaming that the Panthers should be going for two on every touchdown. I think one could even make the argument the Panthers would be an 8-8 team last season at worst, since most of their losses were by only a few points, and by going for 2, not only are you closing that gap, but you are putting more pressure on the opposing offense to score, and then you are taking away pressure from that god-awful defense that gave up all those fourth quarter points.

I think going for two is one of the most underused strategies in the game.

You should go for two whenever you have free points - not just returns for points, but anytime you get the ball on a turnover and score.

You should go for two when you start your scoring drive inside opposing territory because of a long kick or punt return.

You should go for two whenever you are ahead by two or more touchdowns.

You should go for two if you've already converted a 2-point try or if you've already convered two or more 4th down conversions.

You should go for two if you score first.

Going for two is a way to force the other team to score more points than kicking, and forcing the other team to score more points is the most active way to win a game.

Yes, if you suck at converting a two point conversion, then you force yourself to score more points to win than if you kicked PATs, but if you suck at moving the ball 2 yards, you probably suck at lots of other aspects of the game and will end up (or deserve to) losing even if you kick PATs.

I'm not sure teams should be looking at this from an expected points standpoint. If you have a lot of attempts, the best strategy is to do whatever maximizes your expected points. However, with a small number of attempts, it may be better to go with the strategy with a higher floor.

Consider two teams, both with a good two-point threat (Cam Newton or Tim Tebow), and both have, say a 60% chance of converting a 2-pt. For simplicity, assume the kicked extra point is guaranteed. Team A scores ten TD's per game. Team B scores two TD's per game.

Both teams are expected to get 1.2 extra points per TD. But in practice this is impossible, as Led pointed out. You can use a binomial distribution to see which is the better strategy.

If Team A kick every time, they will get 10 points. If Team A goes for two every time, there's a 16% chance they will get fewer than 10, a 20% chance they will get 10, and a 64% chance they will get more than 10 (i.e. that they will succeed more than five times). Clearly, Team A should probably go for two unless specific endgame strategy dictates otherwise.

If Team B kicks every time, they will get 2 points. If they go for two every time, there's a 16% chance they will do worse, a 48% chance they will do about the same, and a 36% chance they will do better. They face the same potential downside that Team A does, but because they have so many fewer trials and are more in danger of an unlucky run, their upside is much much smaller. Plus, because they're scoring fewer total points (and probably in close defensive struggles if they're at all competitive...and if they're not, who cares about what they do?) the loss of those two points is felt more severely. The numbers still slightly favor going for it (there's more upside than downside), but you could make a pretty good argument against.

And this is assuming a probably unrealistic 60% chance. If it was known that a team has a predilection for going for two, opponents would practice their two-point defense more and study their tendencies more and the odds would drop.

If I re-run the numbers assuming the probably oif two-point success is just, say, 54%, then Team A's splits are 28%-24%-48%, and Team B's drop to 21%-50%-29%.

On a serious note, the reality is that most NFL teams look a lot like Team B. The Jets averaged 2.8 touchdowns per game last year. (In 6 games they scored 2 TDs or less.) And only three teams averaged 4 touchdowns per game.

For the Jets, scoring about 3 TDs per game, they'd need to go 2 for 3 to come out ahead in an average game. On that few chances per game, it it worth the risk of coming out the same or worse?

Comparing team A to team B is false framing. Team B must make it's decision based on how the choice affect Team B, not Team A. You said that by adopting a new strategy, they will have fewer points 16% of the time and more points 36%.

A rational actor should take that new strategy because the net expected points are positive.

An emotional actor under prospect theory should still take that strategy, because the upside is over twice as large as the downside (1:2 being the default risk aversion ratio for most people).

The only time it doesn't make sense to adopt the new strategy is if the coach is more risk adverse than the general population. I think that most coaches are. I have no idea if Ryan is. On one hand, he's a "defense and run the ball" kind of coach. On the other hand, he learned football from the guy that invented the Polish Goal Line Defense.

The entire gist of this line of comments is that maximum season points is an oversimplification. The goal is not to score the most points in a season -- it's to win as many games as possible. This is not the same thing as maximizing points scored.

"The goal" in football is a big open question ultimately grounded in preference. I doubt there are many who prefer point differential to win-loss record. But certainly there are people who will prefer post season success to win-loss record or Super Bowl wins to post season wins etc. More likely all sorts of different measurements of success factor in to some objective function that differs by person. Not that that really changes your point that maximizing points may not maximize wins, but rather maximizing wins is just another simplification.

I don't think we have to worry about long term objectives when trying to assess whether or not a team should go for 2. Going for 2 in week 7 does not really affect a team's ability to win a Superbowl outside of it's impact on winning that single game.

So I think strategic decisions like this can be looked at solely on the basis of does it help a team win or lose a single game.

I've already read some comments here regarding injury risk being a factor with someone like Cam Newton. That's a long term strategic risk that seems to be in play. I'm not sure I'm convinced that the risk is really significant enough to worry over, but I don't dismiss it either.

The % above are not for a season they are for a game with 2 TDs. The only impact a usual PAT/2pt conversions can have on the game is the number of points you get out of them. It is the lone criteria by which the strategy can be evaluated.

If there is a way the PAT/2pt decision can affect a game other than the number of resulting points, please point it out. I concede that injury risk is a valid concern, especially for a team like the Panthers.

Why did you choose 2 TDs and 10 TDs as your cases? When's the last competitive game where either team scored 10 TDs? That was just strange.

To be more realistic, let's say in a competitive game - one close enough that extra points matter - a team might score anywhere from 1 to 5 TDs. What we want to know is whether going for a 2 point conversion (at 60% success rate) is more likely to help or hurt their chances of winning. If they get an even number of attempts and go 50%, it's the same as kicking, so we can ignore those cases.

Let's also assume that the benefit of gaining a point (in terms of winning percentage) is the same as the harm from losing a point. That's not true near the end of the game depending on the situation, and it's slightly untrue at all times because of the way football is scored, but it's close enough to true in the first half of almost all games that it doesn't matter.

With one TD, it is clear that a 60% chance of helping their odds to win is better than a 40% chance of hurting them. It's 1.5 times more likely to help than hurt. Go for 2.

With 2 TDs, going for 2 points is 2.25 times more likely to help than hurt. Go for 2.

With 3 TDs, they help their chances to win 65% of the time. That's 1.86 times more likely than hurting their chances. Go for 2.

With 4 TDs, they improve their chances "only" 48% of the time. But they hurt them only 18% of the time. That makes helping 2.67 times more likely than hurting. Go for 2.

With 5 TDs, there's a 68% chance of helping, making it 2.13 more likely to help than hurt their chances of winning. Go for 2.

It matters whether the number of attempts is odd or even, as you can see. But among the odd numbers (and among the evens) the trend is that the more attempts they have, the greater then benefit of going for 2 point conversions.

The effect is smaller as their chance of success drops towards 50%. But it is always there.

I'm not disagreeing with your numbers. But I am disagreeing that a 36% chance of gaining vs. a 16% chance of losing is a bad bet, even in a game expected to be low scoring. It would only be a bad risk if the value of a point gained were somehow much less than the value of a point lost. That can happen with certain scores, especially late in the game. But most of the time, a point is a point, or nearly so. As long as that's (nearly) true, you should go for two if you have a greater than 50% chance of succeeding.

Let's also assume that the benefit of gaining a point (in terms of winning percentage) is the same as the harm from losing a point. That's not true near the end of the game depending on the situation, and it's slightly untrue at all times because of the way football is scored, but it's close enough to true in the first half of almost all games that it doesn't matter.

This is the entire crux of your argument, and I don't think it's necessarily true. Scoring events are so infrequent in football that I don't think you can ever completely ignore the specific point differential.

Moreover the other problem is the fact that because the other team can, in fact, manipulate the pace of the game, risking a situation for more points and failing could, in fact, lead to fewer opportunities than you need to allow statistics to average out.

In other words, if you're, say, down 15, and you go for 2 and fail, so now you're down 9, the other team can bleed the hell out of the clock knowing that they're still up 2 scores.

That can happen with certain scores, especially late in the game. But most of the time, a point is a point, or nearly so. As long as that's (nearly) true, you should go for two if you have a greater than 50% chance of succeeding.

Because a team can bleed nearly half a quarter away (or more) in a specific drive pretty much just by choosing to, I think at best you could say that maybe in the first half you're best going for 2 if you think you have a 50% chance of succeeding.

But I still think it would end up being pointless - at most you're going to gain an extra point or two, and all that would do is just slightly alter the other team's strategy, so in the end, the gain wouldn't be nearly as linear as you think.

The advantages of going for two (if you have a 60% chance) are so large that it does not really matter that all points are not really of equal value. They just have to be nearly equal, maybe to within 50%. As you suggest, that pretty much is true in all first half situations, but only some second half ones.

If an extra point or two either way doesn't matter, why not always kick? Answer: because an extra point either way does matter. Consider:

On your team's likely last drive (assuming there may be an opportunity for the opponent to answer or for you to do an onside kick) these score differentials involve different strategic considerations and/or chances for success.

Down 12 or 13: you must go for a TD, kick an extra point, recover an onside kick, go for a TD, and then kick the extra point. Down 13 is slightly harder because your extra points have to be perfect. For everything else a one-point change either way suggests a different decision on some part of your strategy needed to win or at least get to overtime.

If you aren't better than 50% on two point conversions, some point differentials collapse into the same strategic decisions. But if you are good at them, every point except the one between down 12 and down 13 matters unless the game is already beyond reach.

Variance is related to the probability of winning, just as much as expected number of points is related to it. My point is that people who look only at the latter stat and ignore the former are really not doing a sound analysis.

Yes, I know expected number of points scored is an easy stat to compute. But the relathionship between risk and reward is itself a vital component of strategy planning in any setting.

This discussion has long since been about win percentage, not expected number of points in the game. You're way behind.

In football, and ignoring ties and regular season tiebreakers for the nonce, there are just two possible values for a game: 1 (win) and 0 (loss). In such a system, expected value (aka winning percentage) tells the whole story. Variance literally adds nothing to the description of the distribution.

And in 2011 the average team scored 2.25 TDs a game, so realistically you're only talking about a couple of decisions per game.

I did a quick data dump from Pro Football Reference on scoring margin last year (and please understand this is a rough analysis). There were 268 games played in the NFL in 2011 including the Super Bowl. 129 of those had an ending scoring margin which was larger than 8 points (meaning the loser needed two scores when the final gun sounded), and the average margin of loss was 20 points. I feel very comfortable throwing those out as games where going for two would have made no difference.

No surprise that 3 points and 7 points were most common. Of games decided by 7 & 8 points, on average the losing team scored 18 points- eyeballing the scores it looks like they were scoring around 1.5 TDs a game. Even if we were generous and called that 2 TDs, it's unlikely that going for 2 those extra times would have changed the course of the game b/c the losing team still would have needed a TD at the end to tie/win so there wouldn't have been a change in strategy. You can also make the same case for 6 points, although there are a couple of good candidates for arguments.

The 5 and 4 point games are actually better candidates. Again we're looking at an average of 1.5 TDs or so for the loser, so in these games going for 2 on those TDs may have been advantageous b/c by the time you got to the end of the game you'd be looking to kick a FG instead of having to score a TD.

The 1 and 2 point games also had similar characteristics- but in these cases you're not necessarily talking about a change in strategy, a FG still would have won the game, but an actual change in result. [And again without further research it's impossible to say a lot here b/c I can't tell by just looking how many of these games had 9 or 10 point leads going into the final minute where the Defense played prevent and allowed the offense to score a TD with little or no time left].

Finally you have the 3 point games. Here I believe going for 2 would have had no impact on the endgame strategy because unless the loser scored 3 or more TDs they would still be playing to kick an FG at the end of the game.

What does all this mean? (I'm not quite sure but it was fun!) There definitely were games where going for 2 and making it every time would have changed the strategy and/or the outcome of the game, however when you apply a generous 60% success rate you're reducing that to a very small subset of games. As we all now one game can be the difference between playoffs and not, but in back-testing this strategy against last year's games I don't think we'd find a meaningful difference in the results.

But this is all after the fact, right? I'm sort of guessing here, but I wonder if the dynamics change if a team is going for two upon its first score.

In other words, we can all say that under the usual situation, where coaches only go for two in rare and obvious circumstances, then the above makes sense and we can read from it what we want. But what if a team goes for two on its first TD? And what if it finds success more than 60% of the time? If that's true, then the opponent is in a bit of a bind when it scores its first TD. After all, the 95% kick makes it 7-8, so you're not tied, you're down a point.

I guess I'm saying that looking at things under the current situation and talking about the difference of what a point or two will make is moot because going for two on a regular basis changes to dynamic from the start.

There's a better way to do this, but it's a project. Tabulate the end-of-first-half margins with the resulting chance of winning. That would give you the relationship between a point of margin early in the game and a win.

I suspect that with enough data points, we would find that the marginal benefit of each point is nearly the same in all cases except blowouts. But someone would have to get the data.

Of course, if Tebow's no good at two point conversions, all this is moot.

Ask Mike Vick what it's like playing with broken ribs. The Jets could go for some conversions with Tebow, but the simple reason the Panthers won't (and shouldn't) is that you can get 70%-95% of the value with zero risk of injury by just kicking extra points.

If you think you have a greater chance of converting the 2 pointer than the other team - you should go for it.
If you score first, to challenge the other team to do the same.
If you score last, to win the game instead of tying it.
If you miss, and they score the extra point - you got to do it again anyway to tie.
If you are going to do it, you practice it more than the other teams. So it's a commitment.
Also, if you're the Saints and you just made a miracle play to save the season.
.
If you think you're equal to the other teams, then it won't make much sense though. You'll have to score 3 2 pointers to 'add' a fieldgoal worth of points on the board.

We also have no idea how this would affect the timing of the kickers. Nick Folk came out 68 times last year and only 25 of those were FG attempts. It's asking a lot of a special teams unit (especially the snapper, holder and kicker) to get the timing down right in pressure situations when they're only facing game time conditions once or twice a game.

Points are not all equal/their is diminishing returns. So the difference between 6 and 7 is slightly greater than the difference between 7 and 8. However, early in the game this effect is very small and I'm not sure it's ever that big except in the end game where score effects take over. As far as getting Newton hit an extra time I think thats overstated. 1. every 2 point attempt isn't going to be a Newton run. 2. An extra .2 points is equivalent to about a 15-20 yard play early in a tie game, so pretty significant. The only thing that matters in decisions like these is win probability. So the way to figure out when to go for 2 with say, 60% equity is to take .6*(win probability by adding 2 points)+.4*(win probability adding 0 points) and if its greater than the win probability of adding 1 point then you go for it. If it's not you don't. Thats it.

The really irrational strategy is in college football overtime, where teams routinely kick an extra point to tie. This is one place where going for 2 is clearcut, even if it has lower expected points, because the tying team is forced to take the ball first in the next overtime.

I am surprised at how many people seem predisposed to refute the conclusion of this article. Are we just Tebow-haters, or just instinctively conservative when it comes to football strategy? That being said the game will still dictate weather it is better to go for 1 or 2 in a given situation. Even with Tebow at QB there would be some situations that you would prefer to kick the extra point. Never-the-less, I think the main point of the article is perfectly valid.

Looking back over the discussion we see these reasons to reject the article's conclusions:

1) Expected value in points score is the wrong way to evaluate this strategy.
(This objection is correct, but is dealt with in comments.)
2) You could have an unlucky streak and lose unnecessarily.
(This is bogus. You could get lucky and steal a win, too.)
3) The effect is too small to matter, as measured in points or wins.
(Bogus. It's a moderately high leverage situation. Why not do your best?)
4) It increases your variance - in points scored.
(This is semi-bogus. Points are the wrong measure to work with.)
5) It increases your variance - in wins.
(This is uber-bogus. All wins are equal. Variance doesn't apply.)
6) It can kill or help emotional momentum - this was argued both ways, I think.
(This could be real, in the same way that voodoo could be real.)
7) Coaches should/shouldn't be as risk averse as they are.
(True, if you think coaches aren't optimizing wins, but instead credit/blame.)
8) There are some situations where it doesn't make sense.
(True, but no one says otherwise.)

Oddly enough, no one argued that Tebow wasn't likely to convert at a more than 55% rate.

The upshot is that if you know your team is good (solidly above 50%, let's say) at two-point conversions, you should do them in most situations ... unless you think your team or owner would quit on you if some of them didn't work.

The arguments against are mostly bogus. As always, particular margins late in the game could make this a "must" or "must never" strategy.